On the homotopy of closed manifolds and finite CW-complexes

نویسندگان

چکیده

We study the finite generation of homotopy groups closed manifolds and CW-complexes by relating it to cohomology their fundamental groups. Our main theorems are as follows: when X X is a CW-complex dimension alttext="n"> n encoding="application/x-tex">n alttext="pi 1 left-parenthesis upper X right-parenthesis"> π 1 ( stretchy="false">) encoding="application/x-tex">\pi _1(X) virtually Poincaré duality group alttext="greater-than-or-equal-to n minus 1"> ≥ −<!-- − encoding="application/x-tex">\geq n-1 , then Subscript i Baseline i _i(X) not finitely generated for some alttext="i"> encoding="application/x-tex">i unless equivalent Eilenberg–MacLane space K pi right-parenthesis comma K , encoding="application/x-tex">K(\pi _1(X),1) ; M"> M encoding="application/x-tex">M an -dimensional manifold M _1(M) encoding="application/x-tex">\ge alttext="i less-than-or-equal-to left-bracket slash 2 right-bracket"> ≤<!-- ≤ stretchy="false">[ / 2 stretchy="false">] encoding="application/x-tex">i\leq [n/2] _i(M) generated, itself aspherical manifold. These generalize M. Damian [Trans. Amer. Math. Soc. 361 (2009), pp. 1791–1809] from polycyclic any

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ژورنال

عنوان ژورنال: Proceedings of the American Mathematical Society

سال: 2022

ISSN: ['2330-1511']

DOI: https://doi.org/10.1090/proc/15784